# Solve a Rubik's cube

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Solve a Rubik's cube is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

Create a program that is capable of solving a   Rubik's Cube   as efficiently as possible.

Other names are:

•   Magic Cube
•   Speed Cube
•   Puzzle Cube
•   Cube

You may use any sort of input you wish.

## Go

As in the case of the Kotlin entry, this is a translation of the C++ competition code by Stefan Pochmann.

On the same machine, typical timings for the 100 line dataset are just over 200 milliseconds which is significantly slower than both the Kotlin and C++ code but still acceptable.

The relative slowness may be partly due to maps in Go not being able to accept reference types (such as slices) as a key because they don't support the '==' operator which tests for structural equality. I've therefore had to copy each slice returned by the 'id' function into a forty element array (a value type in Go) and use that as a key instead.

For the single line example, typical timings are around 240 milliseconds which is much faster than Kotlin due, no doubt, to JVM warm up time.

```/**********************************************************************
*
* A cube 'state' is an int array with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/

package main

import (
"bufio"
"fmt"
"log"
"os"
"strings"
"time"
)

type ai = [40]int

var applicableMoves = [5]int{0, 262143, 259263, 74943, 74898}

var phase = 0

var affectedCubies = [6][8]int{
{0, 1, 2, 3, 0, 1, 2, 3},   // U
{4, 7, 6, 5, 4, 5, 6, 7},   // D
{0, 9, 4, 8, 0, 3, 5, 4},   // F
{2, 10, 6, 11, 2, 1, 7, 6}, // B
{3, 11, 7, 9, 3, 2, 6, 5},  // L
{1, 8, 5, 10, 1, 0, 4, 7},  // R
}

func btoi(b bool) int {
if b {
return 1
}
return 0
}

func sliceToAi(s []int) ai {
var a ai
copy(a[:], s)
for i := len(s); i < 40; i++ {
a[i] = -1
}
return a
}

func applyMove(move int, state ai) ai {
turns := move%3 + 1
face := move / 3
for turns != 0 {
turns--
oldState := state
for i := 0; i < 8; i++ {
isCorner := btoi(i > 3)
target := affectedCubies[face][i] + isCorner*12
temp := i + 1
if (i & 3) == 3 {
temp = i - 3
}
killer := affectedCubies[face][temp] + isCorner*12
var orientationDelta int
switch {
case i < 4:
orientationDelta = btoi(face > 1 && face < 4)
case face < 2:
orientationDelta = 0
default:
orientationDelta = 2 - (i & 1)
}
state[target] = oldState[killer]
state[target+20] = oldState[killer+20] + orientationDelta
if turns == 0 {
state[target+20] %= 2 + isCorner
}
}
}
return state
}

func inverse(move int) int {
return move + 2 - 2*(move%3)
}

func id(state ai) ai {
//--- Phase 1: Edge orientations.
if phase < 2 {
return sliceToAi(state[20:32])
}

//-- Phase 2: Corner orientations, E slice edges.
if phase < 3 {
result := state[31:40]
for e := uint(0); e < 12; e++ {
result[0] |= (state[e] / 8) << e
}
return sliceToAi(result)
}

//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if phase < 4 {
result := []int{0, 0, 0}
for e := uint(0); e < 12; e++ {
temp := 2
if state[e] <= 7 {
temp = state[e] & 1
}
result[0] |= temp << (2 * e)
}
for c := uint(0); c < 8; c++ {
result[1] |= ((state[c+12] - 12) & 5) << (3 * c)
}
for i := 12; i < 19; i++ {
for j := i + 1; j < 20; j++ {
result[2] ^= btoi(state[i] > state[j])
}
}
return sliceToAi(result)
}

//--- Phase 4: The rest.
return state
}

func main() {
startTime := time.Now()
aggregateMoves := 0

//--- Define the goal.
goal := [20]string{
"UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR",
}

//--- Load dataset (file name should be passed as a command line argument).
if len(os.Args) != 2 {
log.Fatal("the file name should be passed as a command line argument")
}
file, err := os.Open(os.Args[1])
if err != nil {
log.Fatal(err)
}
defer file.Close()

var lineCount = 0
scanner := bufio.NewScanner(file)
for scanner.Scan() {
line := scanner.Text()
inputs := strings.Fields(line)
lineCount++
phase = 0
totalMoves := 0

//--- Prepare current (start) and goal state.
var currentState ai
var goalState ai
for i := 0; i < 20; i++ {
//--- Goal state.
goalState[i] = i

//--- Current (start) state.
cubie := inputs[i]
for {
idx := -1
for c := 0; c < len(goal); c++ {
if goal[c] == cubie {
idx = c
break
}
}
if idx >= 0 {
currentState[i] = idx
} else {
currentState[i] = 20
}
if currentState[i] != 20 {
break
}
cubie = cubie[1:] + cubie[:1]
currentState[i+20]++
}
}

//--- Dance the funky Thistlethwaite..
nextPhase:
for phase++; phase < 5; phase++ {

//--- Compute ids for current and goal state, skip phase if equal.
currentId := id(currentState)
goalId := id(goalState)
if currentId == goalId {
continue
}

//--- Initialize the BFS queue.
q := []ai{currentState, goalState}

//--- Initialize the BFS tables.
predecessor := make(map[ai]ai)
direction := make(map[ai]int)
lastMove := make(map[ai]int)
direction[currentId] = 1
direction[goalId] = 2

//--- Dance the funky bidirectional BFS...
for {
//--- Get state from queue, compute its ID and get its direction.
oldState := q[0]
q = q[1:]
oldId := id(oldState)
oldDir := direction[oldId]

//--- Apply all applicable moves to it and handle the new state.
for move := 0; move < 18; move++ {
if (applicableMoves[phase] & (1 << uint(move))) != 0 {
//--- Apply the move.
newState := applyMove(move, oldState)
newId := id(newState)
newDir := direction[newId]

//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if (newDir != 0) && (newDir != oldDir) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if oldDir > 1 {
newId, oldId = oldId, newId
move = inverse(move)
}

//--- Reconstruct the connecting algorithm.
algorithm := []int{move}
for oldId != currentId {
algorithm = append(algorithm, 0)
copy(algorithm[1:], algorithm[0:])
algorithm[0] = lastMove[oldId]
oldId = predecessor[oldId]
}
for newId != goalId {
algorithm = append(algorithm, inverse(lastMove[newId]))
newId = predecessor[newId]
}

//--- Print and apply the algorithm.
for i := 0; i < len(algorithm); i++ {
fmt.Printf("%c", "UDFBLR"[algorithm[i]/3])
fmt.Print(algorithm[i]%3 + 1)
fmt.Print(" ")
totalMoves++
currentState = applyMove(algorithm[i], currentState)
}

//--- Jump to the next phase.
continue nextPhase
}

//--- If we've never seen this state (id) before, visit it.
if newDir == 0 {
q = append(q, newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
}
}
}
fmt.Printf(" (moves %d)\n", totalMoves)
aggregateMoves += totalMoves
}
if err := scanner.Err(); err != nil {
log.Fatal(err)
}
endTime := time.Now()
elapsedTime := endTime.Sub(startTime).Nanoseconds() / 1000000
fmt.Println("\nAverage number of moves =", float64(aggregateMoves)/float64(lineCount))
fmt.Println("\nAverage time =", elapsedTime/int64(lineCount), "milliseconds")
}
```
Output:
```Same as Kotlin entry apart, of course, from the timings.
```

## Julia

Translation of: Kotlin
```#=**********************************************************************
*
* A cube 'state' is a vector<int> with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
*********************************************************************=#

const applicablemoves = [0, 262143, 259263, 74943, 74898]

const affectedcubies = [
0 1 2 3 0 1 2 3;   # U
4 7 6 5 4 5 6 7;   # D
0 9 4 8 0 3 5 4;   # F
2 10 6 11 2 1 7 6; # B
3 11 7 9 3 2 6 5;  # L
1 8 5 10 1 0 4 7]  # R

function applymove(move, state)
state2, oldstate2 = deepcopy(state), zeros(Int, length(state))
face, turns = divrem(move, 3) .+ 1
while turns != 0
turns -= 1
oldstate2 .= state2
for i in 1:8
iscorner = i > 4
target = affectedcubies[face, i] + iscorner * 12 + 1
temp = ((i-1) & 3) == 3 ? i - 3 : i + 1
killer = affectedcubies[face, temp] + iscorner * 12 + 1
orientationdelta = i < 5 ? Int(face in [3, 4]) : face < 3 ? 0 : 2 - ((i-1) & 1)
state2[target] = oldstate2[killer]
state2[target + 20] = oldstate2[killer + 20] + orientationdelta
(turns == 0) && (state2[target + 20] %= 2 + iscorner)
end
end
return state2
end

inverse(move) = move + 2 - 2 * (move % 3)

function id(state::Vector{Int}, phase::Int)
#--- Phase 1: Edge orientations.
if phase < 2
return state[21:32]
elseif phase < 3
#-- Phase 2: Corner orientations, E slice edges.
result =  state[32:40]
for e in 0:11
result[1] |= ((state[e + 1] ÷ 8) << e)
end
return result
elseif phase < 4
#--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
result = zeros(Int, 3)
for e in 0:11
result[1] |= state[e + 1] > 7 ? 2 : (state[e + 1] & 1) << (2 * e)
end
for c in 0:7
result[2] |= ((state[c + 12 + 1] - 12) & 5) << (3 * c)
end
for i in 13:19, j in i+1:20
result[3] ⊻= Int(state[i] > state[j])
end
return result
end
#--- Phase 4: The rest.
return state
end

function pochmann(fname)
starttime = time_ns() ÷ 1000000
aggregatemoves = 0
#--- Define the goal.
goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]

#--- Load dataset (file name should be passed as a command line argument).
file = read(fname, String)
linecount = 0
for line in split(strip(file), "\n")
inputs = split(line)
linecount += 1
totalmoves = 0
#--- Prepare current (start) and goal state.
state, goalstate, phase = zeros(Int, 40), zeros(Int, 40), 0
for i in 1:20
#--- Goal state.
goalstate[i] = i - 1

#--- Current (start) state.
cubie = inputs[i]
while true
state[i] = something(findfirst(x -> x .== cubie, goal), 21) - 1
(state[i] != 20) && break
cubie = cubie[2:end] * cubie[1]
state[i + 20] += 1
end
end
#--- Dance the funky Thistlethwaite...
@label nextphase    # preserves phase value, but restarts while loop
while (phase += 1) < 5
#--- Compute ids for current and goal state, skip phase if equal.
currentid = id(state, phase)
goalid = id(goalstate, phase)
currentid == goalid && continue

#--- Initialize the BFS queue.
q = [state, goalstate]
#--- Initialize the BFS tables.
predecessor = Dict{Vector{Int}, Vector{Int}}()
direction = Dict{Vector{Int}, Int}()
lastmove = Dict{Vector{Int}, Int}()
direction[currentid] = 1
direction[goalid] = 2

#--- Dance the funky bidirectional BFS...
while true
#--- Get state from queue, compute its ID and get its direction.
oldstate = popfirst!(q)
oldid = id(oldstate, phase)
olddir = get!(direction, oldid, 0)

#--- Apply all applicable moves to it and handle the new state.
for move in 0:17
if applicablemoves[phase + 1] & (1 << UInt(move)) != 0
#--- Apply the move.
newstate = applymove(move, oldstate)
newid = id(newstate, phase)
newdir = get!(direction, newid, 0)

#--- Have we seen this state (id) from the other direction already?
#--- I.e. have we found a connection?
if (newdir != 0) && (newdir != olddir)
#--- Make oldid represent the forwards
#--- and newid the backwards search state.
if olddir > 1
newid, oldid = oldid, newid
move = inverse(move)
end

#--- Reconstruct the connecting algorithm.
algorithm = [move]
while oldid != currentid
pushfirst!(algorithm, get(lastmove, oldid, 0))
oldid = get!(predecessor, oldid, Int[])
end
while newid != goalid
push!(algorithm, inverse(get!(lastmove, newid, 0)))
newid = get!(predecessor, newid, Int[])
end

#--- Print and apply the algorithm.
for i in 1:length(algorithm)
print("UDFBLR"[algorithm[i] ÷ 3 + 1])
print(algorithm[i] % 3 + 1)
print(" ")
totalmoves += 1
state = applymove(algorithm[i], state)
end

#--- Jump to the next phase.
@goto nextphase
end
#--- If we've never seen this state (id) before, visit it.
if newdir == 0
push!(q, newstate)
direction[newid] = olddir
lastmove[newid] = move
predecessor[newid] = oldid
end
end
move += 1
end
end
end
println(" (moves \$totalmoves)")
aggregatemoves += totalmoves
end
elapsedtime = time_ns() ÷ 1000000 - starttime
println("\nAverage number of moves = \$(aggregatemoves / linecount)")
println("\nAverage time = \$(elapsedtime / linecount) milliseconds")
end

pochmann("rubikdata.txt")
```
Output:

Using the 100-line database:

``` (moves 0)
U1 U2  (moves 2)
U2  (moves 1)
U1  (moves 1)
F1 F2  (moves 2)
F2  (moves 1)
F1  (moves 1)
R1 R2  (moves 2)
R2  (moves 1)
R1  (moves 1)
D1 D2  (moves 2)
D2  (moves 1)
D1  (moves 1)
B1 B2  (moves 2)
B2  (moves 1)
B1  (moves 1)
L1 L2  (moves 2)
L2  (moves 1)
L1  (moves 1)
U2 B3 B2  (moves 3)
L2 U3  (moves 2)
R1 U1  (moves 2)
D3 L3  (moves 2)
D3 L2  (moves 2)
D2 F3 F2  (moves 3)
R2 F3  (moves 2)
R1 F2 F2 R2 F2  (moves 5)
D1 D2 U2  (moves 3)
L1 B2 F2 L2 R2 B2 F2  (moves 7)
L1 L2 D3  (moves 3)
D1 F2  (moves 2)
U2 R3  (moves 2)
L1 L2 U3  (moves 3)
U1 R2  (moves 2)
U1 R3  (moves 2)
F1 U2  (moves 2)
U2 R3 R2  (moves 3)
F2 D1 F3  (moves 3)
F2 D3 D2 U2  (moves 4)
L3 D2 R3  (moves 3)
D2 R3 R2 D3  (moves 4)
F1 R1 B2 B2 R2 B2  (moves 6)
L1 B2 F2  (moves 3)
U1 R2 B3 B2  (moves 4)
R2 F3 R2  (moves 3)
L2 D3 R3 R2  (moves 4)
L2 F3 L2 L2 F2 L2  (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2  (moves 29)
L1 L2 U3 R2  (moves 4)
L3 B3 B2 R3 R2  (moves 5)
B2 U1 R3 R2  (moves 4)
L3 B3 L2  (moves 3)
D1 B2 L3 L2  (moves 4)
B1 B2 R3 F2 F2 R2 F2  (moves 7)
D1 F3 D1 D2  (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2  (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2  (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2  (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2  (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2  (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2  (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2  (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2  (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2  (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2  (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2  (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2  (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2  (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2  (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2  (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2  (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2  (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2  (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2  (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2  (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2  (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2  (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2  (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2  (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2  (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2  (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2  (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2  (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2  (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2  (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2  (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2  (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2  (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2  (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2  (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2  (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2  (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2  (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2  (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2  (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2  (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2  (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2  (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2  (moves 36)

Average number of moves = 16.38

Average time = 65.71 milliseconds
```

## Kotlin

This is a translation of Stefan Pochmann's C++ entry in the 2004 competition which was linked to by the author of the Phix entry. This program won the Judge's prize, finished second overall and (as in the case of the winner) is based on Thistlethwaite's algorithm.

I've adjusted the code to accept input from a file whose name is supplied via a command line argument and, as in the case of the original competition, to calculate the average number of moves for each line in the file and the average time to process each one.

To aid readability I've also inserted spaces between each move in the results and added the total moves needed for each line.

```// version 1.2.21

/**********************************************************************
*
* A cube 'state' is a vector<int> with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/

import java.util.ArrayDeque
import java.io.File

fun Boolean.toInt() = if (this) 1 else 0

typealias AI = ArrayList<Int>

val applicableMoves = intArrayOf(0, 262143, 259263, 74943, 74898)

val affectedCubies = listOf(
intArrayOf(0,  1, 2,  3, 0, 1, 2, 3),  // U
intArrayOf(4,  7, 6,  5, 4, 5, 6, 7),  // D
intArrayOf(0,  9, 4,  8, 0, 3, 5, 4),  // F
intArrayOf(2, 10, 6, 11, 2, 1, 7, 6),  // B
intArrayOf(3, 11, 7,  9, 3, 2, 6, 5),  // L
intArrayOf(1,  8, 5, 10, 1, 0, 4, 7)   // R
)

fun applyMove(move: Int, state: AI): AI {
val state2 = AI(state)  // avoids mutating original 'state'.
var turns = move % 3 + 1
val face = move / 3
while (turns-- != 0) {
val oldState2 = AI(state2)
for (i in 0..7) {
val isCorner = (i > 3).toInt()
val target = affectedCubies[face][i] + isCorner * 12
val temp = if ((i and 3) == 3) i - 3 else i + 1
val killer = affectedCubies[face][temp] + isCorner * 12
val orientationDelta =
if (i < 4) (face in 2..3).toInt()
else if (face < 2) 0
else 2 - (i and 1)
state2[target] = oldState2[killer]
state2[target + 20] = oldState2[killer + 20] + orientationDelta
if (turns == 0) state2[target + 20] %= 2 + isCorner
}
}
return state2
}

fun inverse(move: Int) = move + 2 - 2 * (move % 3)

var phase = 0

fun id(state: AI): AI {
//--- Phase 1: Edge orientations.
if (phase < 2) return AI(state.subList(20, 32))

//-- Phase 2: Corner orientations, E slice edges.
if (phase < 3) {
val result =  AI(state.subList(31, 40))
for (e in 0..11) result[0] = result[0] or ((state[e] / 8) shl e)
return result
}

//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if (phase < 4) {
val result = AI(3)
repeat(3) { result.add(0) }
for (e in 0..11) {
val temp  = (if (state[e] > 7) 2 else (state[e] and 1)) shl (2 * e)
result[0] = result[0] or temp
}
for (c in 0..7) {
val temp =  ((state[c + 12] - 12) and 5) shl (3 * c)
result[1] = result[1] or temp
}
for (i in 12..18) {
for (j in (i + 1)..19) {
result[2] = result[2] xor (state[i] > state[j]).toInt()
}
}
return result
}

//--- Phase 4: The rest.
return state
}

fun main(args: Array<String>) {
val startTime = System.currentTimeMillis()
var aggregateMoves = 0

//--- Define the goal.
val goal = listOf(
"UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"
)

//--- Load dataset (file name should be passed as a command line argument).
val file = File(args[0])
var lineCount = 0
file.forEachLine { line ->
val inputs = line.split(' ')
lineCount++
phase = 0
var totalMoves = 0

//--- Prepare current (start) and goal state.
var currentState = AI(40)
repeat(40) { currentState.add(0) }
val goalState = AI(40)
repeat(40) { goalState.add(0) }
for (i in 0..19) {
//--- Goal state.
goalState[i] = i

//--- Current (start) state.
var cubie = inputs[i]
while (true) {
val idx = goal.indexOf(cubie)
currentState[i] = if (idx >= 0) idx else 20
if (currentState[i] != 20) break
cubie = cubie.substring(1) + cubie[0]
currentState[i + 20]++
}
}

//--- Dance the funky Thistlethwaite...
nextPhase@ while (++phase < 5) {
//--- Compute ids for current and goal state, skip phase if equal.
val currentId = id(currentState)
val goalId = id(goalState)
if (currentId == goalId) continue

//--- Initialize the BFS queue.
val q = ArrayDeque<AI>()
q.addLast(currentState)
q.addLast(goalState)

//--- Initialize the BFS tables.
val predecessor = mutableMapOf<AI, AI>()
val direction = mutableMapOf<AI, Int>()
val lastMove = mutableMapOf<AI, Int>()
direction[currentId] = 1
direction[goalId] = 2

//--- Dance the funky bidirectional BFS...
while (true) {
//--- Get state from queue, compute its ID and get its direction.
val oldState = q.peek()
q.pop()
var oldId = id(oldState)
val oldDir = direction.getOrPut(oldId) { 0 }

//--- Apply all applicable moves to it and handle the new state.
var move = 0
while (move < 18) {
if ((applicableMoves[phase] and (1 shl move)) != 0) {
//--- Apply the move.
val newState = applyMove(move, oldState)
var newId = id(newState)
var newDir = direction.getOrPut(newId) { 0 }

//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if ((newDir != 0) && (newDir != oldDir)) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if (oldDir > 1) {
val temp = newId
newId = oldId
oldId = temp
move = inverse(move)
}

//--- Reconstruct the connecting algorithm.
val algorithm = AI()
algorithm.add(move)
while (oldId != currentId) {
val tempI = lastMove.getOrPut(oldId) { 0 }
algorithm.add(0, tempI)
val tempAI = predecessor.getOrPut(oldId) { AI() }
oldId = tempAI
}
while (newId != goalId) {
val tempI = lastMove.getOrPut(newId) { 0 }
algorithm.add(inverse(tempI))
val tempAI = predecessor.getOrPut(newId) { AI() }
newId = tempAI
}

//--- Print and apply the algorithm.
for (i in 0 until algorithm.size) {
print("UDFBLR"[algorithm[i] / 3])
print(algorithm[i] % 3 + 1)
print(" ")
totalMoves++
currentState = applyMove(algorithm[i], currentState)
}

//--- Jump to the next phase.
continue@nextPhase
}

//--- If we've never seen this state (id) before, visit it.

if (newDir == 0) {
q.addLast(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
move++
}
}
}
println(" (moves \$totalMoves)")
aggregateMoves += totalMoves
}
val elapsedTime = System.currentTimeMillis() - startTime
println("\nAverage number of moves = \${aggregateMoves.toDouble() / lineCount}")
println("\nAverage time = \${elapsedTime / lineCount} milliseconds")
}
```
Output:

Using the original dataset of 100 lines, the results were as follows (time doesn't mean much but is typical for my modest machine):

```U1 U2  (moves 2)
U2  (moves 1)
U1  (moves 1)
F1 F2  (moves 2)
F2  (moves 1)
F1  (moves 1)
R1 R2  (moves 2)
R2  (moves 1)
R1  (moves 1)
D1 D2  (moves 2)
D2  (moves 1)
D1  (moves 1)
B1 B2  (moves 2)
B2  (moves 1)
B1  (moves 1)
L1 L2  (moves 2)
L2  (moves 1)
L1  (moves 1)
U2 B3 B2  (moves 3)
L2 U3  (moves 2)
R1 U1  (moves 2)
D3 L3  (moves 2)
D3 L2  (moves 2)
D2 F3 F2  (moves 3)
R2 F3  (moves 2)
R1 F2 F2 R2 F2  (moves 5)
D1 D2 U2  (moves 3)
L1 B2 F2 L2 R2 B2 F2  (moves 7)
L1 L2 D3  (moves 3)
D1 F2  (moves 2)
U2 R3  (moves 2)
L1 L2 U3  (moves 3)
U1 R2  (moves 2)
U1 R3  (moves 2)
F1 U2  (moves 2)
U2 R3 R2  (moves 3)
F2 D1 F3  (moves 3)
F2 D3 D2 U2  (moves 4)
L3 D2 R3  (moves 3)
D2 R3 R2 D3  (moves 4)
F1 R1 B2 B2 R2 B2  (moves 6)
L1 B2 F2  (moves 3)
U1 R2 B3 B2  (moves 4)
R2 F3 R2  (moves 3)
L2 D3 R3 R2  (moves 4)
L2 F3 L2 L2 F2 L2  (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2  (moves 29)
L1 L2 U3 R2  (moves 4)
L3 B3 B2 R3 R2  (moves 5)
B2 U1 R3 R2  (moves 4)
L3 B3 L2  (moves 3)
D1 B2 L3 L2  (moves 4)
B1 B2 R3 F2 F2 R2 F2  (moves 7)
D1 F3 D1 D2  (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2  (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2  (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2  (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2  (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2  (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2  (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2  (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2  (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2  (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2  (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2  (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2  (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2  (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2  (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2  (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2  (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2  (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2  (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2  (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2  (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2  (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2  (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2  (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2  (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2  (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2  (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2  (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2  (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2  (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2  (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2  (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2  (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2  (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2  (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2  (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2  (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2  (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2  (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2  (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2  (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2  (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2  (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2  (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2  (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2  (moves 34)
```
```
Average number of moves = 16.72

Average time = 127 milliseconds
```

When run with a file containing the single line:

UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL

a typical result was:

```U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)

Average number of moves = 29.0

Average time = 522 milliseconds
```

## Nim

Translation of: Kotlin
```#[
**********************************************************************
*
* A cube 'state' is a sequence of ints with 40 entries, the first
* 20 are a permutation of {0,...,19} and describe which cubie is
* at a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************
]#

import deques, os, strformat, strutils, tables, times

const

ApplicableMoves = [0, 262143, 259263, 74943, 74898]

AffectedCubies = [[0,  1, 2,  3, 0, 1, 2, 3],  # U
[4,  7, 6,  5, 4, 5, 6, 7],  # D
[0,  9, 4,  8, 0, 3, 5, 4],  # F
[2, 10, 6, 11, 2, 1, 7, 6],  # B
[3, 11, 7,  9, 3, 2, 6, 5],  # L
[1,  8, 5, 10, 1, 0, 4, 7]]  # R

type State = seq[int]

func initState(n: Natural = 0): State = newSeq[int](n)

var phase: Natural

proc slicetoState(s: openArray[int]): State =
result.setLen(40)
for i, val in s: result[i] = val
for i in s.len..39: result[i] = -1

proc id(state: State): State =

case phase
of 1: # Phase 1: Edge orientations.
result = sliceToState(state[20..31])

of 2: # Phase 2: Corner orientations, E slice edges.
var res = state[31..39]
for e in 0..11:
res[0] = res[0] or state[e] shr 3 shl e
result = sliceToState(res)

of 3: # Phase 3: Edge slices M and S, corner tetrads, overall parity.
var res = @[0, 0, 0]
for e in 0..11:
let temp = if state[e] > 7: 2 else: (state[e] and 1) shl (2 * e)
res[0] = res[0] or temp
for c in 0..7:
res[1] = res[1] or ((state[c + 12] - 12) and 5) shl (3 * c)
for i in 12..18:
for j in (i + 1)..19:
res[2] = res[2] xor ord(state[i] > state[j])
result = sliceToState(res)

else: # Phase 4: The rest.
result = state

proc applyMove(move: int; state: State): State =
result = state
var turns = move mod 3 + 1
let face = move div 3
while turns != 0:
dec turns
var oldState = result
for i in 0..7:
let isCorner = ord(i > 3)
let target = AffectedCubies[face][i] + isCorner * 12
let temp = if (i and 3) == 3: i - 3 else: i + 1
let killer = AffectedCubies[face][temp] + isCorner * 12
let orientationDelta =
if i < 4: ord(face in 2..3)
elif face < 2: 0
else: 2 - (i and 1)
result[target] = oldState[killer]
result[target + 20] = oldState[killer + 20] + orientationDelta
if turns == 0:
result[target + 20] = result[target + 20] mod (2 + isCorner)

func inverse(move: int): int = move + 2 - 2 * (move mod 3)

let startTime = cpuTime()
var aggregateMoves = 0

# Define the goal.
const Goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]

# Load dataset (file name should be passed as a command line argument).
if paramCount() == 0: quit "Missing file name", QuitFailure
var lineCount = 0
for line in paramStr(1).lines():
let inputs = line.splitWhitespace()
inc lineCount
var totalMoves = 0

# Prepare current (start) and goal state.
var currentState, goalState = initState(40)
for i in 0..19:
# Goal state.
goalState[i] = i
# Current (start) state.
var cubie = inputs[i]
while true:
let idx = Goal.find(cubie)
currentState[i] = if idx >= 0: idx else: 20
if currentState[i] != 20: break
cubie = cubie[1..^1] & cubie[0]
inc currentState[i + 20]

# Dance the funky Thistlethwaite...
phase = 1
while phase < 5:
block doPhase:

# Compute ids for current and goal state, skip phase if equal.
let currentId = id(currentState)
let goalId = id(goalState)
if currentId == goalId: break doPhase

# Initialize the BFS queue.
var q = [currentState, goalState].toDeque

# Initialize the BFS tables.
var predecessor: Table[State, State]
var direction, lastMove: Table[State, int]
direction[currentId] = 1
direction[goalId] = 2

# Dance the funky bidirectional BFS.
while true:
# Get state from queue, compute its ID and get its direction.
let oldState = q.popFirst()
var oldId = id(oldState)
let oldDir = direction[oldId]

# Apply all applicable moves to it and handle the new state.
var move = 0
while move < 18:
if (ApplicableMoves[phase] and (1 shl move)) != 0:
# Apply the move.
let newState = applyMove(move, oldState)
var newId = id(newState)
let newDir = direction.getOrDefault(newId, 0)

# Have we seen this state (id) from the other direction already?
# I.e. have we found a connection?
if newDir != 0 and newDir != oldDir:
# Make oldId represent the forwards and newId the backwards search state.
if oldDir > 1:
swap newId, oldId
move = inverse(move)

# Reconstruct the connecting algorithm.
var algorithm: State = @[move]
while oldId != currentId:
algorithm.insert(lastMove.mgetOrPut(oldId, 0), 0)
oldId = predecessor.mgetOrPut(oldId, initState())
while newId != goalId:
algorithm.add inverse(lastMove.mgetOrPut(newId, 0))
newId = predecessor.mgetOrPut(newId, initState())

# Print and apply the algorithm.
for step in algorithm:
stdout.write "UDFBLR"[step div 3], step mod 3 + 1, ' '
inc totalMoves
currentState = applyMove(step, currentState)

# Jump to the next phase.
break doPhase

# If we've never seen this state (id) before, visit it.
if newdir == 0:
q.addLast(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId

inc move

inc phase

echo &" (moves {totalMoves})"
inc aggregateMoves, totalMoves

let elapsedTime = cpuTime() - startTime
echo &"\nAverage number of moves = {aggregateMoves / lineCount}"
echo &"\nAverage time = {elapsedTime * 1000 / lineCount.toFloat:.2f} milliseconds"
```
Output:

We compiled the program with command `nim c -d:danger --gc:arc -d:lto`, which means no runtime checks, ARC memory management and link time optimization.

When run with the original dataset of 100 lines, we got:

```U1 U2  (moves 2)
U2  (moves 1)
U1  (moves 1)
F1 F2  (moves 2)
F2  (moves 1)
F1  (moves 1)
R1 R2  (moves 2)
R2  (moves 1)
R1  (moves 1)
D1 D2  (moves 2)
D2  (moves 1)
D1  (moves 1)
B1 B2  (moves 2)
B2  (moves 1)
B1  (moves 1)
L1 L2  (moves 2)
L2  (moves 1)
L1  (moves 1)
U2 B3 B2  (moves 3)
L2 U3  (moves 2)
R1 U1  (moves 2)
D3 L3  (moves 2)
D3 L2  (moves 2)
D2 F3 F2  (moves 3)
R2 F3  (moves 2)
R1 F2 F2 R2 F2  (moves 5)
D1 D2 U2  (moves 3)
L1 B2 F2 L2 R2 B2 F2  (moves 7)
L1 L2 D3  (moves 3)
D1 F2  (moves 2)
U2 R3  (moves 2)
L1 L2 U3  (moves 3)
U1 R2  (moves 2)
U1 R3  (moves 2)
F1 U2  (moves 2)
U2 R3 R2  (moves 3)
F2 D1 F3  (moves 3)
F2 D3 D2 U2  (moves 4)
L3 D2 R3  (moves 3)
D2 R3 R2 D3  (moves 4)
F1 R1 B2 B2 R2 B2  (moves 6)
L1 B2 F2  (moves 3)
U1 R2 B3 B2  (moves 4)
R2 F3 R2  (moves 3)
L2 D3 R3 R2  (moves 4)
L2 F3 L2 L2 F2 L2  (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2  (moves 29)
L1 L2 U3 R2  (moves 4)
L3 B3 B2 R3 R2  (moves 5)
B2 U1 R3 R2  (moves 4)
L3 B3 L2  (moves 3)
D1 B2 L3 L2  (moves 4)
B1 B2 R3 F2 F2 R2 F2  (moves 7)
D1 F3 D1 D2  (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2  (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2  (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2  (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2  (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2  (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2  (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2  (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2  (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2  (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2  (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2  (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2  (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2  (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2  (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2  (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2  (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2  (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2  (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2  (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2  (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2  (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2  (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2  (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2  (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2  (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2  (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2  (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2  (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2  (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2  (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2  (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2  (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2  (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2  (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2  (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2  (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2  (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2  (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2  (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2  (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2  (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2  (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2  (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2  (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2  (moves 34)```
```Average number of moves = 16.72

Average time = 52.03 milliseconds```

When run with a file containing the single line:

UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL

a typical result was:

```U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)

Average number of moves = 29.0

Average time = 69.01 milliseconds```

## Phix

### cfop

Uses brute-force (width/highscore-first) Fridrich-steps (ie cross,f2l,oll,pll).
Not the fastest (see THRESHOLD) or shortest results (see thistlethwaite) but the code is pretty easy to follow.
The final stage (pll) would probably benefit the most from being replaced with standard algorithms.
While technically this works under pwa/p2js, you should expect a blank screen for nearly 3 minutes.

```--
-- demo\rosetta\rubik_cfop.exw
--
-- Each stage uses a workspace of moves tried so far, ranked by score.
-- We repeatedly take the best scoring so far and try more moves, storing
-- those results in a second/new workspace. The THRESHOLD value below
-- determines the minimum number we should examine before discarding a
-- workspace and switching to the new (one move longer) one. We only ever
-- switch on change of score, and obviously the first workspace is empty,
-- and the next new workspace has a maximum of 12 entries (+/-90 by 6),
-- both of which will force earlier switches.
--
with javascript_semantics
constant THRESHOLD =   100000 -- 100000 -- very slow (100s), best results
--                      10000 --  10000 -- slow (10s), reasonable results
--   1000 -- fast (1s), fairly poor results
--    100 -- (counter-productive/slower)

string init ="""
---YYY--------
---YYY--------
---YYY--------
BBBRRRGGGOOO--
BBBRRRGGGOOO--
BBBRRRGGGOOO--
------WWW-----
------WWW-----
------WWW-----

"""
-- numbering:
--  1..15:   ---456--------\n
--  16..30:  ---901--------\n   -- U
--  31..45:  ---456--------\n
--  46..60:  678901234567--\n
--  61..75:  123456789012--\n   -- LFRB
--  76..90:  678901234567--\n
--  91..105: ------789-----\n
--  106..120:------234-----\n   -- D
--  121..136:------789-----\n\n

if length(init)!=136 then ?9/0 end if

--
-- TIP: Wrap a cube with blank paper, and write
--      the numbers on it, to derive these sets.
--
constant centres = {20,62,65,68,71,113}

constant edges = {{  4,  5,  6,57,56,55},   -- ie YYY/OOO
{  6, 21, 36,54,53,52},   --    YYY/GGG
{ 34, 35, 36,49,50,51},   --    YYY/RRR
{  4, 19, 34,46,47,48},   --    YYY/BBB
{ 51, 66, 81,52,67,82},   --    RRR/GGG
{ 54, 69, 84,55,70,85},   --    GGG/OOO
{ 57, 72, 87,46,61,76},   --    OOO/BBB
{ 48, 63, 78,49,64,79},   --    BBB/RRR
{ 97, 98, 99,82,83,84},   --    WWW/GGG
{ 99,114,129,85,86,87},   --    WWW/OOO
{127,128,129,78,77,76},   --    WWW/BBB
{ 97,112,127,81,80,79}}   --    WWW/RRR

constant corners = {{ 4, 57,46},{34,48, 49},{36,51,52},{ 6,54,55},
--   YOB/UBL     YBR/UFL     YRG/UFR    YGO/UBL
{76,129,87},{78,79,127},{81,82,97},{84,85,99}}
--   BWO/DBL     BRW/DFL     RGW/DFR    GOW/DFL

constant facing_corners = {-16,-14,16,14}, -- (nb not 14,16)
facing_edges   = {-15,  1,15,-1},
fce = facing_corners&facing_edges,
rotations = {
-- up (clockwise):
{{57,54,51,48},   -- clockwise corners
{46,55,52,49},   -- anticlockwise corners
{47,56,53,50}},  -- middle edges
-- left
{{ 4,49,127, 87},
{57,34, 79,129},
{19,64,128, 72}},
-- front
{{34,52, 97, 78},
{48,36, 82,127},
{35,67,112, 63}},
-- right
{{36,55,99,81},
{51, 6,85,97},
{21,70,98,66}},
-- back
{{ 6,46,129,84},
{54, 4, 76,99},
{ 5,61,114,69}},
-- down
{{82,85,76,79},
{81,84,87,78},
{83,86,77,80}}}

--Up/Left/Front/Right/Back/Down
enum U=1,L=2,F=3,R=4,B=5,D=6,Dbl=#08,Shift=#10
constant U2 = U+Dbl, F2 = F+Dbl, /*R2 = R+Dbl, B2 = B+Dbl,*/ D2 = D+Dbl,
Us = U+Shift, Fs = F+Shift, Bs = B+Shift, Rs = R+Shift, Ds = D+Shift

enum CROSS,F2L,OLL,PLL

integer f2l = 0         -- (28==done)
integer edge_score = 0  -- (0..12 for f2l [as U cleared],
--  0..24 for oll and pll stages)

function score(string cube, integer stage)
integer res = 0, c, cc, k
f2l = 0
for i=1 to length(centres) do
c = centres[i]
cc = cube[c]
for j=1 to length(fce) do -- (the 8 next to c)
k = c+fce[j]
if cube[k]=cc then
res += 1
f2l += (stage>CROSS and k>=61)
end if
end for
end for
-- give extra credit for edges paired with corners
edge_score = 0  -- += (0|1|2) for the 12 edges:
if stage>CROSS then
for i=1 to length(edges) do
sequence ei = edges[i]  -- as 123
--                      --    456
-- then if {1,4}=={2,5} then edge_score += 1,
-- plus if {2,5}=={3,6} then edge_score += 1.
edge_score += (cube[ei[1]]=cube[ei[2]] and
cube[ei[4]]=cube[ei[5]]) +
(cube[ei[2]]=cube[ei[3]] and
cube[ei[5]]=cube[ei[6]])
end for
end if
return res
end function

function oll_score(string cube)
-- (should only be invoked if f2l==28)
integer res = 0     -- (true if res=8)
integer cu = centres[U]
if cube[cu]!='Y' then ?9/0 end if
for i=1 to length(fce) do
integer fcei = fce[i]
res += (cube[cu+fcei]='Y')
end for
return res
end function

function rotate_face(string cube, integer face)
--
-- face is 1..6 for clockwise (ULFRBD),
-- plus #08(Dbl) for a 180 (clockwise),
-- plus #10(Shift) for anti-clockwise.
--
integer dbl = 1+(and_bits(face,Dbl)=Dbl)
bool cw = 1-floor(face/Shift)
face = remainder(face,Dbl)
integer cf = centres[face]
sequence rf = {sq_add(facing_corners,cf),
sq_add(facing_edges,cf)}
&rotations[face]
for d=1 to dbl do
for i=1 to length(rf) do
sequence rfi = rf[i]
if cw then rfi = reverse(rfi) end if
integer rfi1 = cube[rfi[1]]
for j=1 to 3 do
cube[rfi[j]] = cube[rfi[j+1]]
end for
cube[rfi[4]] = rfi1
end for
end for
return cube
end function

function apply_moves(string cube, sequence moves)
for i=1 to length(moves) do
cube = rotate_face(cube,moves[i])
end for
return cube
end function

constant ULFRBD = "ULFRBD"

function moves_to_string(sequence moves)
-- convert eg {1,20,11} to "UR'F2"
string res = ""
integer l = length(moves)
for i=1 to l do
integer face = moves[i]
integer dbl = and_bits(face,Dbl)=Dbl
bool anticw = floor(face/Shift)
face = remainder(face,Dbl)
res &= ULFRBD[face]
if dbl then
res &= '2'
elsif anticw then
res &= '\''
end if
end for
res &=sprintf("  (%d move%s)     ",{l,iff(l=1?"":"s")})
return res
end function

--
-- The seen dictionary.
--  Without this, since it uses a breadth/highscore-first
--  algorithm, after f2l (for instance) it would probably
--  just do U and U' as the new high scores, forever.
--  (The THRESHOLD constant mitigates that to some extent)
--
integer seen = new_dict()

function solve_stage(string cube, integer stage)
atom t1 = time()+1
string moves = "", moves2
sequence workspace, w2, init
integer wslen, high = 1,
s, c2c = 0, o = 0
bool done

if stage=CROSS then
--
-- first, blank out all corners, and
-- all edges without a white on them.
--
for i=1 to length(rotations) do
for j=1 to 2 do -- (just corners)
for k=1 to 4 do
cube[rotations[i][j][k]]='-'
end for
end for
end for
for i=1 to length(edges) do
integer {?,m1,?,?,m2,?} = edges[i]
if cube[m1]!='W'
and cube[m2]!='W' then
cube[m1] = '-'
cube[m2] = '-'
end if
end for
wslen = 8
s = score(cube,CROSS)
done = (s=8)
elsif stage=F2L then
--
-- first, blank out all pieces with a yellow
--
for i=1 to length(corners) do
integer {c1,c2,c3} = corners[i]
if cube[c1]='Y'
or cube[c2]='Y'
or cube[c3]='Y' then
cube[c1] = '-'
cube[c2] = '-'
cube[c3] = '-'
end if
end for
for i=1 to length(edges) do
integer {?,m1,?,?,m2,?} = edges[i]
if cube[m1]='Y'
and cube[m2]='Y' then
cube[m1] = '-'
cube[m2] = '-'
end if
end for
wslen = 57+12
s = score(cube,F2L)
done = (f2l=28)
else
wslen = 77+24
s = score(cube,stage)
if f2l!=28 then ?9/0 end if
if stage=OLL then
done = (oll_score(cube)=8)
else -- (stage=PLL)
done = (s=48)
end if
end if
if not done then
workspace = repeat({},wslen)
w2 = deep_copy(workspace)
init = cube
workspace[high] = {""}
destroy_dict(seen,justclear:=1)
integer move_count = 1
while 1 do
if workspace[high]={} then
while high and workspace[high]={} do high -= 1 end while
if high=0 or (stage!=CROSS and c2c>THRESHOLD) then
move_count += 1
workspace = w2
w2 = repeat({},wslen)
c2c = 0
high = wslen
while workspace[high]={} do high -= 1 end while
end if
end if
moves = workspace[high][1]
workspace[high] = workspace[high][2..\$]
cube = apply_moves(init,moves)
for face=U to D do
-- (originally this loop did 180s as well, but that
--  gave them far too much dominance, esp during pll.
--  instead we now coalese those that survive a 90.)
for m=0 to Shift by Shift do
integer mi = face+m
sequence cube2 = rotate_face(cube,mi)
if getd_index(cube2,seen)=0 then
putd(cube2,0,seen)
s = score(cube2,stage)
if stage=CROSS then
done = (s=8)
elsif stage=F2L then
done = (f2l=28)
else
if f2l=28 then
o = oll_score(cube2)
else
o = 0
end if
if stage=OLL then
done = (o=8)
else
done = (s=48)
end if
end if
moves2 = moves
if length(moves2) and moves2[\$]=mi then
moves2[\$] = face+Dbl
else
moves2 &= mi
end if
if done then
destroy_dict(seen,justclear:=1)
return moves2
end if
s += 1+edge_score*2+o
w2[s] = append(w2[s],moves2)
c2c += 1
end if
end for
end for
if time()>t1 and platform()!=JS then
printf(1,"working... %d moves, %d positions\r",{move_count,dict_size(seen)})
t1 = time()+1
if get_key()=#1B then exit end if
end if
end while
end if
return ""   -- (already solved case)
end function

constant stage_desc = { "make cross",
"solve first two layers",
"orientate last layer",
"permute last layer" }

procedure main()
string cube
sequence moves
integer total_moves = 0
atom t0 = time()

-- "hardest case" from http://www.cube20.org
moves = {F, Us, F2, Ds, B, U, Rs, Fs, L, Ds,
Rs, Us, L, U, Bs, D2, Rs, F, U2, D2}
cube = apply_moves(init,moves)
if length(moves)<=20 then
printf(1,"scramble: %s\n",{moves_to_string(moves)})
end if

puts(1,substitute(cube,"-"," "))

for stage=CROSS to PLL do
moves = solve_stage(cube, stage)
total_moves += length(moves)
cube = apply_moves(cube,moves)
printf(1,"%s: %s\n",{stage_desc[stage],moves_to_string(moves)})
if length(moves) then
puts(1,substitute(cube,"-"," "))
end if
end for
printf(1,"\nsolution of %d total moves found in %3.2fs\n",{total_moves,time()-t0})
end procedure
main()
```
Output:

The "hardest case" from http://www.cube20.org with a high threshold. You can try this manually. Disclaimer: the results are not always quite as good as this!

```scramble: FU'F2D'BUR'F'LD'R'U'LUB'D2R'FU2D2  (20 moves)
ROB
BYG
GRO
YYOYYBYYRYYG
RBOBRGOGRGOB
WWOWWBWWRWWG
OGB
RWO
GBR

make cross: DLBRFL  (6 moves)
BRB
YYG
YYY
ROBRBRGOYOGW
OBRBRYRGYGOB
RBYORGOGOBOW
WWW
WWW
GWG

solve first two layers: FUL'R'FLRF'LRB'R'U'BU'B'U'B  (18 moves)
RYG
OYR
YYY
BYRGGOBYOYBY
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW

orientate last layer: R'F'U'FUR  (6 moves)
YYY
YYY
YYY
GGBRRGOOOBBR
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW

permute last layer: RU'L'UR'U2LU'L'U2LU'  (12 moves)
YYY
YYY
YYY
BBBRRRGGGOOO
BBBRRRGGGOOO
BBBRRRGGGOOO
WWW
WWW
WWW

solution of 42 total moves found in 81.33s
```

### thistlethwaite

Translation/de-golf(hrumph) of Tomas Sirgedas' winning entry from http://tomas.rokicki.com/cubecontest as held in 2004.
Faster and shorter solutions (in most cases) than cfop, however probably nigh on impossible to debug/enhance...

```--
-- demo\rosetta\rubik_tomas.exw
--
with javascript_semantics
function xor_string(string s)
return xor_bits(s[1],xor_bits(s[2],iff(length(s)=3?s[3]:'!')))
end function

function xor_all(sequence s)
for i=1 to length(s) do
s[i] = xor_string(s[i])
end for
return s
end function

constant d1 = xor_all(split("UF DF UB DB UR DR UL DL FR FL BR BL UFR DBR UBL DFL DLB ULF DRF URB"))
-- This is Mike Reid's notation, 12 sides then 8 corners, which may be rotated - hence we xor the
-- characters for fast lookup. The above string represents a cube in the solved state.

constant d2 = {18,12,17,15,0, 9,1,8,16,14,19,13,2,10,3,11,12,18,13,19,4,8,5,10,
14,16,15,17,6,11,7,9,17,12,19,14,6, 0,4, 2,18,15,16,13,1,7,3, 5}
--?sort(d2): (0..11 appear twice, 12..19 appear thrice - edges/corners is pretty much all I can say)

constant d3 = {13,16,15,1,3,
19,18,17,4,6}
-- these apppear to be swapped during initialisation, dunno why...

integer cur_phase, search_mode, history_idx
sequence history_mov = repeat(0,48),
history_rpt = repeat(0,48),
depth_to_go,
hash_table = repeat(repeat(6,6912),48)
-- (hash_table can/should be preserved for different problems)

sequence cubelet_pos = repeat(0,48),
cubelet_twi = repeat(0,48)

procedure rot(integer cur_phase)
if cur_phase<4 then
for i=0 to 3 do
integer di = cur_phase*8+i+1,
j = d2[di]+1,
k = d2[di+4]+1
cubelet_twi[j] = mod(cubelet_twi[j]+2-mod(i,2),3)
cubelet_twi[k] = xor_bits(cubelet_twi[k],cur_phase<2)
end for
end if

for i=0 to 6 do
integer di = cur_phase*8+i+1,
j = d2[di+(i!=3)]+1,
k = d2[di]+1
-- swap(cubelet[j]], cubelet[k]);
{cubelet_pos[j],cubelet_pos[k]} = {cubelet_pos[k],cubelet_pos[j]}
{cubelet_twi[j],cubelet_twi[k]} = {cubelet_twi[k],cubelet_twi[j]}
end for
end procedure

function hashf()
int ret = 0;
switch cur_phase do
case 0:
for i=0 to 10 do
ret += ret + cubelet_twi[i+1]
end for
return ret;
case 1:
for i=0 to 6 do
ret = ret*3 + cubelet_twi[i+12+1]
end for
for i=0 to 10 do
ret += ret + (cubelet_pos[i+1]>7)
end for
return ret-7;
case 2:
sequence inva = repeat(0,48),
b = repeat(0,48)
for i=0 to 7 do
integer ci12p = cubelet_pos[i+12+1],
ci12p3 = and_bits(ci12p,3)
if ci12p<16 then
inva[ci12p3+1] = ret
ret += 1
else
b[i-ret+1] = ci12p3
end if
end for
for i=0 to 6 do
ret += ret + (cubelet_pos[i+1]>3);
end for
for i=0 to 6 do
ret += ret + (cubelet_pos[i+12+1]>15);
end for
integer ib2 = xor_bits(inva[b[1]+1],inva[b[2]+1])*2,
ib3 = xor_bits(inva[b[1]+1],inva[b[3]+1]),
ib4 = xor_bits(inva[b[1]+1],inva[b[4]+1])
return ret*54 + ib2 + (ib3 > ib4) - 3587708
end switch
for i=0 to 4 do
ret *= 24;
for cp=0 to 3 do
for k=0 to cp-1 do
if cubelet_pos[i*4+cp+1] < cubelet_pos[i*4+k+1] then
ret += cp + iff(cp=3?cp:0)
end if
end for
end for
end for
return floor(ret/2)
end function

function do_search(integer dpt)
integer h = hashf(),
q = (floor(cur_phase/2)*19+8)*power(2,7),
hmq = mod(h,q)+1,
hfq = floor(h/q)+1,
d = (dpt < hash_table[cur_phase+1][hmq] or
dpt < hash_table[cur_phase+4+1][hfq])

if d xor search_mode then
if search_mode then
if dpt <= depth_to_go[h+1] then
return not h;
else
depth_to_go[h+1] = dpt;
end if
end if

hash_table[cur_phase+1][hmq] = min(hash_table[cur_phase+1][hmq],dpt);
hash_table[cur_phase+5][hfq] = min(hash_table[cur_phase+5][hfq],dpt);

for k=0 to 5 do
for i=0 to 3 do
rot(k)
if (k>=cur_phase*2 or i=1) and i<=2 then
history_idx += 1
history_mov[history_idx] = k
history_rpt[history_idx] = i
if do_search(dpt-search_mode*2+1) then return 1 end if
history_idx -= 1
end if
end for
end for
end if
return 0
end function

function pack_moves()
string moves = ""
integer n = 0, curr, last, last_rpt
if history_idx!=0 then
-- add a dummy move to trigger the last move print:
last = xor_bits(history_mov[history_idx],1) -- F<->B, etc
history_idx += 1
history_mov[history_idx] = last
history_rpt[history_idx] = 0
last = history_mov[1]
last_rpt = 0
for i=1 to history_idx do
curr = history_mov[i]
if curr!=last then
-- coalesce eg F1F2 to F' (unless you wanna fix do_search()!)
if last_rpt then
moves &= "FBRLUD"[last+1] & {"","2","'"}[last_rpt]
n += 1
end if
last = curr
last_rpt = history_rpt[i]+1
else
last_rpt = mod(last_rpt+history_rpt[i]+1,4)
end if
end for
end if
return {moves,n,iff(n=1?"":"s")}
end function

function tomas(sequence args)
search_mode = 0
history_idx = 0
depth_to_go = repeat(0,5*power(2,20))

for i=0 to 19 do
cubelet_pos[i+1] = i
end for
for i=0 to 3 do
cur_phase = i
{} = do_search(0)
end for
args = split(args)
for i=0 to 19 do
string s = args[i+1]    -- (may be rotated, eg RU or UR)
integer p = find(xor_string(s),d1)
if p=0 then ?9/0 end if -- sensible message(bad args)?
cubelet_pos[i+1] = p-1
int x = max(find('U',s), find('D',s));
cubelet_twi[i+1] = iff(x!=0 ? x-1 : s[1]>'F')
end for
for i=0 to 4 do
integer j = d3[i+1]+1,
k = d3[i+6]+1
-- swap(cubelet[j], cubelet[k]);
{cubelet_pos[j],cubelet_pos[k]} = {cubelet_pos[k],cubelet_pos[j]}
{cubelet_twi[j],cubelet_twi[k]} = {cubelet_twi[k],cubelet_twi[j]}
end for
search_mode = 1;
for cp=0 to 3 do
cur_phase = cp
for i=0 to 19 do
if do_search(i) then exit end if
end for
end for
return pack_moves()
end function

printf(1,"%s (%d move%s)\n",tomas("UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL"))
```
Output:
```UF'R'FB2R2B2LD2L2DLR2U'F2UF2U2F2L2UF2DF2U2R2U2R2B2D2R2F2L2B2D2 (35 moves)
```

The distributed copy of demo\rosetta\rubik_cfop.exw also contains routines to convert between my 136-character cube and reid notation, and demo\rosetta\rubik_tomas.exw also contains the full 100-long test set from the original competition.

## Wren

Translation of: Kotlin

Wren has a similar problem to Go in that Lists cannot be used as Map keys. Worse still Wren doesn't support fixed size arrays so I've had to convert the Lists to space delimited Strings which is an expensive operation.

Despite this, the script is taking an average of just over a second to calculate the number of moves for each line which is probably not too bad for an interpreted language.

```/**********************************************************************
*
* A cube 'state' is an int array with 40 entries, the first 20
* are a permutation of {0,...,19} and describe which cubie is at
* a certain position (regarding the input ordering). The first
* twelve are for edges, the last eight for corners.
*
* The last 20 entries are for the orientations, each describing
* how often the cubie at a certain position has been turned
* counterclockwise away from the correct orientation. Again the
* first twelve are edges, the last eight are corners. The values
* are 0 or 1 for edges and 0, 1 or 2 for corners.
*
**********************************************************************/

import "os" for Process
import "io" for File

var applicableMoves= [0, 262143, 259263, 74943, 74898]

var phase = 0

var affectedCubies = [
[0,  1, 2,  3, 0, 1, 2, 3],   // U
[4,  7, 6,  5, 4, 5, 6, 7],   // D
[0,  9, 4,  8, 0, 3, 5, 4],   // F
[2, 10, 6, 11, 2, 1, 7, 6],   // B
[3, 11, 7,  9, 3, 2, 6, 5],   // L
[1,  8, 5, 10, 1, 0, 4, 7]    // R
]

var btoi = Fn.new { |b| (b) ? 1 : 0 }

var applyMove = Fn.new { |move, origState|
var state = origState[0..-1] // make copy so don't mutate original
var turns = move%3 + 1
var face = (move/3).floor
while (turns != 0) {
turns = turns - 1
var oldState = state[0..-1]  // make a copy prior to mutation
for (i in 0..7) {
var isCorner = btoi.call(i > 3)
var target = affectedCubies[face][i] + isCorner*12
var temp = (i&3 == 3) ? i - 3 : i + 1
var killer = affectedCubies[face][temp] + isCorner*12
var orientationDelta
if (i < 4) {
orientationDelta = btoi.call(face > 1 && face < 4)
} else if (face < 2) {
orientationDelta = 0
} else {
orientationDelta = 2 - (i&1)
}
state[target] = oldState[killer]
state[target+20] = oldState[killer+20] + orientationDelta
if (turns == 0) state[target+20] = state[target+20] % (2 + isCorner)
}
}
return state
}

var inverse = Fn.new { |move| move + 2 - 2*(move%3) }

var id = Fn.new { |state|
//--- Phase 1: Edge orientations.
if (phase < 2) return state[20...32]

//--- Phase 2: Corner orientations, E slice edges.
if (phase < 3) {
var result = state[31...40]
for (e in 0..11) result[0] = result[0] | ((state[e]/8).floor << e)
return result
}

//--- Phase 3: Edge slices M and S, corner tetrads, overall parity.
if (phase < 4) {
var result = [0, 0, 0]
for (e in 0..11) {
var temp = ((state[e] > 7) ? 2 : state[e] & 1) << (2 * e)
result[0] = result[0] | temp
}
for (c in 0..7) {
var temp = ((state[c + 12] - 12) & 5) << (3 * c)
result[1] = result[1] | temp
}
for (i in 12..18) {
for (j in i+1..19) result[2] = result[2] ^ btoi.call(state[i] > state[j])
}
return result
}

//--- Phase 4: The rest.
return state
}

var startTime = System.clock
var aggregateMoves = 0

//--- Define the goal.
var goal = ["UF", "UR", "UB", "UL", "DF", "DR", "DB", "DL", "FR", "FL", "BR", "BL",
"UFR", "URB", "UBL", "ULF", "DRF", "DFL", "DLB", "DBR"]

//--- Load dataset (file name should be passed as a command line argument).
if (Process.arguments.count != 1) {
Fiber.abort("The file name should be passed as a command line argument.")
}

var lines = File.read(Process.arguments[0]).split("\n")
if (lines[-1] == "") lines.removeAt(-1) // if there's a final blank line remove it
var lineCount = lines.count
for (line in lines) {
var inputs = line.split(" ")
phase = 0
var totalMoves = 0

//--- Prepare current (start) and goal state.
var currentState = List.filled(40, 0)
var goalState = List.filled(40, 0)
for (i in 0..19) {
//--- Goal state.
goalState[i] = i

//--- Current (start) state.
var cubie = inputs[i]
while (true) {
var idx = -1
for (c in 0...goal.count) {
if (goal[c] == cubie) {
idx = c
break
}
}
currentState[i] = (idx >= 0) ? idx : 20
if (currentState[i] != 20) break
cubie = cubie[1..-1] + cubie[0]
currentState[i+20] = currentState[i+20] + 1
}
}

//--- Dance the funky Thistlethwaite..
phase = phase + 1
while (phase < 5) {
var nextPhase = false
//--- Compute ids for current and goal state, skip phase if equal.
var currentId = id.call(currentState).join(" ")
var goalId = id.call(goalState).join(" ")
if (currentId != goalId) {
//--- Initialize the BFS queue.
var q = [currentState, goalState]

//--- Initialize the BFS tables.
var predecessor = {}
var direction = {}
var lastMove = {}
direction[currentId] = 1
direction[goalId] = 2

//--- Dance the funky bidirectional BFS...
while (true) {
//--- Get state from queue, compute its ID and get its direction.
var oldState = q[0]
q = q[1..-1]
var oldId = id.call(oldState).join(" ")
var oldDir = direction[oldId]
if (oldDir == null) {
oldDir = 0
direction[oldId] = 0
}

//--- Apply all applicable moves to it and handle the new state.
var move = 0
while (move < 18) {
if ((applicableMoves[phase] & (1 << move)) != 0) {
//--- Apply the move.
var newState = applyMove.call(move, oldState)
var newId = id.call(newState).join(" ")
var newDir = direction[newId]
if (newDir == null) {
newDir = 0
direction[newId] = 0
}

//--- Have we seen this state (id) from the other direction already?
//--- I.e. have we found a connection?
if (newDir != 0 && newDir != oldDir) {
//--- Make oldId represent the forwards
//--- and newId the backwards search state.
if (oldDir > 1) {
var t = newId
newId = oldId
oldId = t
move = inverse.call(move)
}

//--- Reconstruct the connecting algorithm.
var algorithm = [move]
while (oldId != currentId) {
var t = lastMove[oldId]
if (t == null) {
t = 0
lastMove[oldId] = 0
}
algorithm.insert(0, t)
oldId = predecessor[oldId]
if (oldId == null) {
oldId = ""
predecessor[oldId] = ""
}
}
while (newId != goalId) {
var t = lastMove[newId]
if (t == null) {
t = 0
lastMove[newId] = 0
}
algorithm.add(inverse.call(t))
newId = predecessor[newId]
if (newId == null) {
newId = ""
predecessor[newId] = ""
}
}

//--- Print and apply the algorithm.
for (i in 0...algorithm.count) {
System.write("UDFBLR"[(algorithm[i]/3).floor])
System.write(algorithm[i]%3 + 1)
System.write(" ")
totalMoves = totalMoves + 1
currentState = applyMove.call(algorithm[i], currentState)
}

nextPhase = true
break
}

//--- If we've never seen this state (id) before, visit it.
if (newDir == 0) {
q.add(newState)
direction[newId] = oldDir
lastMove[newId] = move
predecessor[newId] = oldId
}
}
move  = move + 1
}
if (nextPhase) break
}
}
phase = phase + 1
}
System.print(" (moves %(totalMoves))")
aggregateMoves = aggregateMoves + totalMoves
}
var endTime = System.clock
var elapsedTime = ((endTime - startTime) * 1000).round
System.print("\nAverage number of moves = %(aggregateMoves/lineCount)")
System.print("\nAverage time = %(elapsedTime/lineCount) milliseconds")
```
Output:

Using the original dataset of 100 lines, the results were as follows:

```U1 U2  (moves 2)
U2  (moves 1)
U1  (moves 1)
F1 F2  (moves 2)
F2  (moves 1)
F1  (moves 1)
R1 R2  (moves 2)
R2  (moves 1)
R1  (moves 1)
D1 D2  (moves 2)
D2  (moves 1)
D1  (moves 1)
B1 B2  (moves 2)
B2  (moves 1)
B1  (moves 1)
L1 L2  (moves 2)
L2  (moves 1)
L1  (moves 1)
U2 B3 B2  (moves 3)
L2 U3  (moves 2)
R1 U1  (moves 2)
D3 L3  (moves 2)
D3 L2  (moves 2)
D2 F3 F2  (moves 3)
R2 F3  (moves 2)
R1 F2 F2 R2 F2  (moves 5)
D1 D2 U2  (moves 3)
L1 B2 F2 L2 R2 B2 F2  (moves 7)
L1 L2 D3  (moves 3)
D1 F2  (moves 2)
U2 R3  (moves 2)
L1 L2 U3  (moves 3)
U1 R2  (moves 2)
U1 R3  (moves 2)
F1 U2  (moves 2)
U2 R3 R2  (moves 3)
F2 D1 F3  (moves 3)
F2 D3 D2 U2  (moves 4)
L3 D2 R3  (moves 3)
D2 R3 R2 D3  (moves 4)
F1 R1 B2 B2 R2 B2  (moves 6)
L1 B2 F2  (moves 3)
U1 R2 B3 B2  (moves 4)
R2 F3 R2  (moves 3)
L2 D3 R3 R2  (moves 4)
L2 F3 L2 L2 F2 L2  (moves 6)
F1 R1 B3 D3 B2 D3 L3 U2 L3 U2 L2 U2 L2 U3 R2 U1 F2 L2 U2 B2 L2 F2 U2 L2 U2 F2 D2 F2 U2  (moves 29)
L1 L2 U3 R2  (moves 4)
L3 B3 B2 R3 R2  (moves 5)
B2 U1 R3 R2  (moves 4)
L3 B3 L2  (moves 3)
D1 B2 L3 L2  (moves 4)
B1 B2 R3 F2 F2 R2 F2  (moves 7)
D1 F3 D1 D2  (moves 4)
R1 B3 D1 R2 F3 L1 U2 F2 D3 B2 D1 L3 U1 F2 R2 U1 L2 U1 F2 U2 R2 U3 F2 U3 F2 D2 F2 L2 F2 L2 F2 U2 F2 D2 L2  (moves 35)
F1 R1 U3 D1 B3 U3 D2 L3 B2 R1 F2 D3 L3 U2 R2 D1 R2 B2 U2 L2 U3 U2 F2 U2 L2 B2 R2 D2 R2 D2 B2 L2 F2 U2  (moves 34)
U1 R1 F3 L1 R2 U3 L1 D2 F2 U3 L3 L2 U1 F2 D3 F2 F2 U2 D2 L2 U2 F2 R2 F2 D2 R2 U2  (moves 27)
R1 D3 R3 F3 R1 D3 F2 U1 R3 D2 U1 R3 F2 U1 L2 U3 F2 U1 B2 D2 L2 D3 F2 F2 U2 F2 D2 L2 U2 L2 F2 L2 U2 R2  (moves 34)
D2 R1 B1 L1 F3 U2 D3 L2 R1 D3 B2 U1 F2 L3 F2 U3 B2 U3 B2 L2 U3 B2 U3 F2 U2 F2 U2 L2 F2 R2 B2 D2 L2 D2 F2  (moves 35)
B3 U2 L1 F3 F2 U1 R3 D1 F2 R3 D3 B2 R3 B2 U1 F2 U3 R2 U1 R2 U3 R2 L2 F2 U2 R2 F2 D2 R2 B2 U2 R2 B2  (moves 33)
L1 F3 L2 D3 U1 F3 L1 B2 R1 U1 D1 B2 R3 U1 L2 U1 B2 U1 F2 U3 L2 D1 F2 U3 F2 U2 D2 R2 U2 L2 F2 R2 U2 F2 R2  (moves 35)
F1 R3 U2 F3 B2 U1 L1 U1 R3 B2 U1 R3 R2 U3 L2 U1 B2 U2 R2 U3 L2 U3 F2 L2 U2 F2 U2 B2 L2 D2 L2 F2 L2 F2 U2  (moves 35)
U2 D3 B3 U1 L2 D1 R1 U3 L3 D2 U1 R3 U3 B2 D3 R2 F2 U3 F2 U3 U2 B2 D2 B2 L2 F2 R2 D2 R2  (moves 29)
D2 L3 U3 F3 B2 U3 L1 U2 R3 D2 L3 U2 L2 U3 R2 B2 D3 F2 R2 U3 U2 L2 U2 F2 U2 D2 R2 F2 U2 B2 D2  (moves 31)
F1 L1 U1 L1 B3 U3 L1 F2 L1 B2 F2 U3 L3 F2 D3 B2 D3 R2 U1 F2 U3 L2 U3 U2 F2 D2 B2 U2 F2 R2 F2 L2  (moves 32)
B1 L1 U3 F3 B2 U1 L3 B2 R3 L3 U3 L3 D2 B2 D3 F2 L2 U2 R2 U3 F2 U3 F2 L2 U2 B2 L2 U2 B2 F2 R2 U2 F2  (moves 33)
F2 L3 F1 D3 B3 B2 U3 R1 D3 U3 L3 L2 R2 U3 B2 D1 B2 U3 R2 U3 F2 L2 F2 L2 U2 F2 B2 R2 B2 L2  (moves 30)
D3 F3 U1 B2 U3 L1 D1 R3 U3 F2 L3 U1 F2 U2 L2 U3 L2 B2 R2 L2 D1 F2 F2 L2 U2 F2 L2 U2 R2 D2 B2 R2 L2  (moves 33)
F2 R3 U2 F3 U2 L2 B2 D1 F2 R3 B2 D1 L3 D2 R2 B2 D1 R2 B2 U1 L2 B2 R2 B2 R2 D2 L2 D2 F2 L2 B2 L2 F2  (moves 33)
U1 R3 F3 D3 R3 B2 L3 D1 F2 U1 R3 L2 U1 B2 D1 L2 U3 R2 U1 L2 U3 F2 U3 F2 U2 B2 L2 D2 L2 U2 R2 F2  (moves 32)
F1 R1 F1 D3 B3 F3 U1 R2 F2 U1 L3 U1 F2 U2 R2 U1 R2 U3 L2 U3 D2 L2 F2 L2 F2 U2 B2 U2 L2 F2  (moves 30)
F3 R3 L2 B3 U1 B2 U1 F2 U2 B2 R3 D2 L3 B2 U1 F2 U3 L2 U1 B2 D3 L2 U1 L2 U2 L2 D2 R2 F2 D2 F2 U2 R2 U2  (moves 34)
D1 B3 D2 L1 F3 U3 F2 D2 L3 F2 L3 D3 L3 D1 L2 B2 U3 R2 U1 R2 U3 L2 U3 L2 D2 R2 D2 F2 R2 F2 L2 D2 U2 F2 U2  (moves 35)
U1 B1 D1 R3 F3 U1 B2 R1 U3 L1 D3 B2 U1 R3 U2 F2 L2 U3 R2 U1 B2 D3 B2 U1 L2 F2 U2 D2 L2 U2 B2 R2 B2 L2 D2 L2  (moves 36)
U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)
U1 B2 L1 B3 F3 U1 F2 B2 R2 D3 R3 U3 L3 B2 U1 F2 U3 F2 U3 L2 U2 F2 R2 B2 R2 U2 F2 U2 F2 U2 F2  (moves 31)
U1 B1 U3 D1 F3 U2 D3 R3 D1 U1 L1 F2 L3 D2 L2 U1 F2 B2 R2 U3 F2 U1 L2 U2 R2 F2 D2 F2 U2 L2 B2 U2 F2  (moves 33)
D1 F3 U2 R1 B3 L1 B2 R1 U3 L2 D3 F2 R3 L2 D2 L2 D3 L2 F2 U3 F2 B2 D2 L2 B2 L2 B2 D2 L2 F2 U2 F2 U2  (moves 33)
R1 B1 D3 F3 D1 R3 D3 B2 L2 B2 U2 L3 L2 U2 B2 L2 U2 F2 U3 U2 F2 L2 D2 L2 B2 U2 R2 F2 L2 B2  (moves 30)
U1 D2 F1 L1 B3 D1 B2 D3 L2 R1 D3 L2 U2 R3 D2 F2 U3 F2 R2 U1 B2 U1 F2 U3 B2 R2 U2 L2 U2 B2 D2 F2 L2 B2 F2 U2  (moves 36)
U1 L1 D1 L1 F3 L1 U1 L3 U3 L1 D1 R3 F2 U2 R2 U1 F2 U2 F2 L2 D1 F2 U3 F2 U2 R2 D2 F2 R2 B2 L2 B2 D2 B2  (moves 34)
L3 D3 U1 F3 U2 F2 D3 R3 B2 D3 U3 L3 R2 U2 L2 D3 R2 U1 L2 U2 F2 U3 F2 U3 U2 L2 U2 R2 B2 R2 B2 U2 F2 U2  (moves 34)
L1 B1 U2 D1 F3 B2 U3 R3 D2 U3 L2 U3 L3 F2 U3 R2 U1 F2 R2 L2 D3 F2 F2 B2 L2 D2 F2 R2 D2 B2 R2 F2 L2  (moves 33)
L1 B1 U3 F3 U1 L2 D3 L1 B2 R1 L3 U3 L3 U3 L2 D3 L2 U1 L2 B2 F2 U3 L2 D2 L2 U2 R2 F2 D2 B2 U2 R2 U2  (moves 33)
F1 U1 B3 F3 B2 U2 D3 L3 U3 L3 U3 R2 D3 B2 D2 L2 U3 R2 U2 F2 U3 F2 L2 D2 L2 R2 F2 L2 U2 L2 D2 U2 F2 U2  (moves 34)
D1 L3 R1 F2 U2 F3 U3 F2 D3 L3 D2 L3 U2 L3 D1 L2 U3 R2 D1 B2 U1 L2 R2 U2 L2 D2 B2 R2 F2 L2 D2 U2 F2 U2  (moves 34)
L2 R3 D1 F3 D3 L1 U3 L3 D2 L3 B2 L2 U1 R2 U2 F2 U3 F2 L2 F2 L2 B2 U2 R2 U2 R2 B2 U2 B2  (moves 29)
L2 U2 R1 B3 F3 U1 L1 D3 F2 U2 R3 U2 L3 L2 U2 L2 D2 L2 F2 U3 F2 U2 L2 U2 B2 U2 R2 D2 R2 B2  (moves 30)
L2 F1 U2 F3 D3 R3 U1 D3 L3 D1 U1 L3 R2 D3 R2 F2 D2 B2 U3 F2 U1 F2 D2 L2 B2 U2 L2 U2 R2 B2 F2 U2  (moves 32)
F3 D2 F3 L2 B2 D3 L2 U3 B2 L3 L2 F2 L2 D3 L2 B2 U3 L2 L2 U2 F2 D2 L2 D2 L2 B2 L2 F2 L2 U2  (moves 30)
F3 R2 U3 F3 U3 R3 D2 R2 D1 F2 U2 L3 D3 L2 D3 R2 U1 F2 U3 L2 U1 F2 L2 B2 D2 B2 L2 F2 U2 L2 F2 D2  (moves 32)
B1 R1 U1 D3 F3 R2 U1 L2 R2 D2 B2 U3 L3 R2 F2 U1 L2 B2 U1 F2 U3 L2 U3 R2 U2 F2 D2 F2 L2 B2 L2 U2 F2  (moves 33)
L3 D3 U1 B3 L2 F2 D3 L3 R1 U1 R3 L2 D3 F2 R2 U3 F2 R2 U3 L2 D2 R2 U2 B2 U2 B2 L2 U2 R2 F2 U2  (moves 31)
L1 F3 L2 R1 B3 L1 U3 L1 R1 D3 F2 D1 R3 B2 R2 U1 F2 L2 D1 R2 F2 D2 L2 R2 B2 R2 B2 U2 L2 U2  (moves 30)
U1 F1 U3 L1 B3 D1 L2 B2 R1 D3 R3 F2 L3 U3 F2 B2 L2 U3 B2 D3 L2 U3 L2 D2 R2 F2 D2 L2 F2 D2 F2  (moves 31)
D2 L3 U1 F3 U1 D3 L1 F2 D3 R3 F2 U3 R3 L2 U1 L2 U3 L2 U1 F2 L2 U1 R2 U3 F2 U2 L2 D2 B2 U2 L2 F2 U2 F2 U2  (moves 35)
F3 L2 F3 U1 L1 U1 D2 L3 U3 L3 B2 U1 F2 U1 F2 D2 R2 U3 L2 U2 F2 U3 R2 F2 D2 L2 D2 R2 F2 U2 F2 U2 F2 U2  (moves 34)
U2 L3 B3 U2 R3 U3 L2 B2 U1 R3 R2 D3 R2 U1 R2 U3 F2 U1 F2 U3 F2 U2 L2 F2 R2 F2 D2 L2 D2 L2 B2  (moves 31)
F1 B1 R3 F3 U3 F3 B2 D1 B2 R1 U3 L1 U2 L3 F2 U3 F2 R2 U1 R2 U2 B2 D3 F2 U3 F2 B2 L2 U2 F2 L2 D2 B2 F2 L2 B2  (moves 36)
B2 D3 B3 U2 B2 D3 L3 D1 R1 U2 L3 L2 U3 B2 U1 B2 D2 R2 U3 F2 U3 U2 L2 U2 F2 D2 F2 U2 B2 L2 D2 F2 R2 F2  (moves 34)

Average number of moves = 16.72

Average time = 1005.78 milliseconds
```

When run with a file containing the single line:

UL DL RF UB FD BR DB UF DR UR BL FL FDR BLU DLB URB RUF FLD BRD FUL

a typical result was:

```U3 F1 L1 F3 B2 U1 B2 R2 D1 R1 U2 L3 U1 F2 R2 U3 L2 U3 B2 F2 R2 F2 B2 U2 R2 F2 L2 U2 L2  (moves 29)

Average number of moves = 29

Average time = 665 milliseconds
```